Using a (defined) set of inventory balance equations and an objective function we find two optimal linear replenishment policies for a two echelon supply chain. The first, locally optimal policy is the so-called echelon order-up-to policy. The second, globally optimal policy, is a novel inventory control policy we have not seen in the literature before. We show that it economically dominates the locally optimal policy. There are arbitrary lead-times at each echelon and the demand process is assumed to be ARMA(p,q), thus our investigation is of a rather general nature.